MOSFET

Problem $1$: The problem is about MOSFET in a DC circuit.

For manual calculations consider the following NMOS parameters: $k_n^{\text{'}}=0\mathrm{.}1m\frac{A}{V^2},V_{TH}=0\mathrm{.}9V$ and $=0.$

$1.$a Let $\frac{W}{L}=10.$ We want the transistor to be in Saturation mode with $I_D=0\mathrm{.}9mA$ and $V_{DS}=2\mathrm{.}1$V$.$ What should be $R_D$ and $R_s?[$Hint: Find first the required value of $V_{GS}].$

$1.$b Now we want the transistor to be in Triode mode with $I_D=0\mathrm{.}4mA$ and $V_{DS}=0\mathrm{.}5V.$ What should be $\frac{W}{L},R_D$ and $R{s}_s?[$Hint: Find first an inequality condition for $V_{GS}.$ Then pick up any suitable specific value for $V_{GS}.$ You will then be able to determine all the rest$].$

Problem $2$: The problem is about MOSFET CS Amplifier.

The Common$-$Source amplifier $($shown below$)$ uses a PMOS transistor that has $k_p^{\text{'}}=0\mathrm{.}11m\frac{A}{V^2},V_{TH}=-0\mathrm{.}92V$ and $=0\mathrm{.}01[V^{-1}].$ The bias voltage is $V_G=3V.$ We also have: $V_{DD}=5V$ and $R_D=3K.$

$2.$a Neglect the effect of nonzero $$ on the amplifier's DC conditions. We want $I_D=0\mathrm{.}3mA$ and that the PMOS be in Saturation mode. What should be the value of W$/$L$?$ Draw the small$-$signal diagram and compute $R_{in}$ and the voltage gain $($considering the effect of $).$

$2.$b Now we want to modify $V_G$ and $\frac{W}{L}$ such that the voltage gain obtained in $2.$a becomes $9$ times larger, without changing any other circuit parameters and without changing $I_D.$ Can it be done? If so$,$ specify how. Hint: For PMOS the overdrive voltage $V_{GS}-V_{TH}$ is negative. Also the small$-$signal model of NMOS and PMOS are identical $($including the dependent current source current direction$).$